## Introduction

The Z-score is used for the detection of univariate outliers based on normal distribution. If the Z-score falls outside of the range of -3 to +3, then the data point is considered an outlier. The Z-score also calculates the probability of a data point being an outlier.

### What is an outlier?

In statistics, an outlier is a data point that differs significantly from other observations.

An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set. An outlier can cause serious problems in statistical analyses, since standard procedures assume that all of the data fit a symmetric distribution.

Determining whether or not an observation is an outlier is often done using automatic procedures that use statistics, such as standard deviation, to find unusual observations. These procedures generally have trouble with outliers because the definition of an outlier is that it does not fit well with the rest of the data.

### What are the types of outliers?

An outlier is an observation point that is distant from other observations. Outliers can occur in one dimension (univariate outliers) or in multiple dimensions (multivariate outliers). There are three main types of univariate outliers:

- Standard deviation based: These are outliers that are a certain number of standard deviations away from the mean. Usually, this number is 1.5 or 3.0 standard deviations.
- Absolute value based: These are outliers that are a certain number of units away from the mean. For example, you could say that all points more than 2 units away from the mean are outliers.
- Percentile based: These are outliers that are a certain percentage of observations away from the mean. For example, you could say that all points more than 95% percent of the other observations are outliers.

The Z-score method

The Z-score method of outlier detection is a statistical method that is used for detecting outliers in a data set that is normally distributed. The Z-score method is also known as the standard score method. The Z-score method is used to find the distance between a data point and the mean of the data set.

How is the Z-score method used for outlier detection?

The Z-score method is a statistical technique used for outlier detection. It is based on the idea of comparing the distribution of a data set to a normal distribution, and computing a z-score for each data point. Data points with a z-score beyond a certain threshold are considered outliers.

There are advantages and disadvantages to using the Z-score method for outlier detection. One advantage is that it is relatively simple to implement and understand. A disadvantage is that it requires the data set to be normally distributed, which may not always be the case.

In general, the Z-score method is a useful tool for outlier detection, but it is important to be aware of its limitations.

### What are the advantages and disadvantages of the Z-score method?

There are advantages and disadvantages to using the Z-score method to detect univariate outliers.

Advantages:

-The Z-score is a mathematical method that is objective, consistent and easy to use.

-It is also relatively simple to understand and calculate.

-The Z-score can be used for data that is normally distributed, which is common in many real-world situations.

Disadvantages:

-One drawback of the Z-score method is that it can be less effective for data that is not normal or near normal.

-Another potential drawback is that it does not take into account the context or meaning of the data, which can sometimes be important in detecting outliers.

## TheIQR method

The IQR method is used for detection univariate outliers based on normal distribution. The idea behind this method is to first calculate the interquartile range (IQR), and then use this range to identify outliers. This method is very robust and can be used on data that is not normally distributed.

### How is the IQR method used for outlier detection?

The interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q3 − Q1.

Outliers may be caused by variability in the measurement process. They may also indicate experimental error. The presence of outliers often causes problems for statistical tests, such as ANOVA; therefore it is important to detect and either remove them from the data set or treat them in some special way. Outliers can occur by chance in any distribution but they often indicate either measurement error or make the distribution non-normal.

There are many methods for finding outliers; however most are classified as either univariate or multivariate. The simplest approach to identifying outliers is to examine a graph of the data, using graphical techniques to identify points that lie well outside the overall pattern of the rest of the data. Another approach is to calculate summary statistics for location (mean, median) and spread (standard deviation, interquartile range) and identify points that lie well outside these summary statistics. However, these methods are only suitable for data that are normally distributed; if the data are not normal then other methods are available.

The IQR method is a simple yet powerful way of outlier detection. It is based on the idea that if a point lies outside of the normal range of values (i.e. beyond the 25th and 75th percentiles), then it is an outlier. The IQR method is therefore particularly well suited to data that are approximately normally distributed.

### What are the advantages and disadvantages of the IQR method?

One advantage of the IQR method is that it is relatively simple to calculate and interpret. This makes it a good choice for data that are not normaly distributed. Additionally, the IQR method is less affected by outliers than other methods, such as the standard deviation.

However, there are also some disadvantages to using the IQR method. One is that it can be difficult to know if a data set is normaly distributed. Another is that the results of the IQR method can be influenced by a few extreme values.

## Conclusion

There are many ways to detect outliers, but the most common method is based on the normal distribution. Univariate outliers are values that fall outside of the normal range for a given data set. To calculate the normal range, you need to know the mean and standard deviation of the data set. Once you have these values, you can use the following formula to identify outliers:

Outlier = X < (Mean – 2*Standard Deviation) or X > (Mean + 2*Standard Deviation)

If a value falls outside of this range, it is considered an outlier. This method is not perfect, but it is a good way to identify potential outliers in your data set.